Certainly! Let's find the area of a circle whose circumference is [tex]\( 29 \frac{1}{3} \)[/tex] cm.
### Step-by-Step Solution
1. Convert the given mixed fraction to a decimal:
The given circumference is [tex]\( 29 \frac{1}{3} \)[/tex] cm. We convert the mixed fraction [tex]\( 29 \frac{1}{3} \)[/tex] to a decimal:
[tex]\[
29 \frac{1}{3} = 29 + \frac{1}{3} = 29 + 0.3333\ldots = 29.3333\ldots \text{ cm}
\][/tex]
2. Use the formula for the circumference of a circle to find the radius:
The circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[
C = 2 \pi r
\][/tex]
Where [tex]\( r \)[/tex] is the radius of the circle. Solving for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
Substitute the given circumference:
[tex]\[
r = \frac{29.3333\ldots}{2 \pi}
\][/tex]
3. Calculate the radius:
By substituting the known value, we find the radius:
[tex]\[
r \approx 4.6685 \text{ cm}
\][/tex]
4. Use the formula for the area of a circle:
The area [tex]\( A \)[/tex] of a circle is given by:
[tex]\[
A = \pi r^2
\][/tex]
Using the radius we found earlier.
5. Calculate the area:
Substitute the radius [tex]\( r \approx 4.6685 \)[/tex] cm into the area formula:
[tex]\[
A \approx \pi (4.6685)^2
\][/tex]
[tex]\[
A \approx 68.47199329464651 \text{ square cm}
\][/tex]
### Conclusion
The area of the circle with a circumference of [tex]\( 29 \frac{1}{3} \)[/tex] cm is approximately [tex]\( 68.47199329464651 \)[/tex] square cm.
